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\includegraphics[max width=\textwidth, alt={}, center]{9e129863-5994-4e17-81f8-e139515998d1-3_666_956_1231_593} The diagram shows the curve \(y = x ^ { 2 } \ln x\) and its minimum point \(M\).

1. Find the exact values of the coordinates of \(M\).
2. Find the exact value of the area of the shaded region bounded by the curve, the \(x\)-axis and the line \(x = \mathrm { e }\).